In many applications, the need arises to solve one or more systems of simultaneous linear algebraic equations (SLAEs) whose coefficient matrices comprise only numerical elements. Such applications include engineering and simulation computer codes. Solutions of the SLAE are typically obtained by using the well-known Gaussian elimination method. Therefore, prior methods typically would solve two such SLAE systems S1 and S2, and compare their solutions. However, such methods may not always work if one or both of the SLAEs are ill-conditioned and/or the numerical precision used in computations is not high enough.
Furthermore, such methods are generally not adapted to solving a set of SLAEs whose coefficient matrix elements are algebraic expressions, and for which the solution will, in general, be in algebraic form.